partialSum

formal source

  20/-- Finite partial sum (0..n-1) of the gap coefficients (evaluated at z=1).
  21This stays purely algebraic here; convergence and identification with
  22`log(1 + 1/φ)` can be proved in a companion module that imports analysis. -/
  23noncomputable def partialSum (n : ℕ) : ℝ :=
  24  (Finset.range n).sum (fun i => coeff i)
  25
  26/-- Generating functional F(z) := log(1 + z/φ).  -/
  27noncomputable def F (z : ℝ) : ℝ := Real.log (1 + z / phi)
  28
  29/-- The master gap value as the generator at z=1. -/
  30noncomputable def f_gap : ℝ := F 1
  31@[simp] lemma f_gap_def : f_gap = Real.log (1 + 1 / phi) := rfl
  32
  33end GapSeries
  34
  35namespace Curvature
  36
  37/-- Curvature-closure constant δ_κ used in the α pipeline.
  38Defined here as the exact rational/π expression from the voxel seam count. -/
  39noncomputable def deltaKappa : ℝ := - (103 : ℝ) / (102 * Real.pi ^ 5)
  40
  41/-- The predicted dimensionless inverse fine-structure constant
  42α^{-1} = 4π·11 − (ln φ + δ_κ).
  43This is a pure expression-level definition (no numerics here). -/
  44noncomputable def alphaInvPrediction : ℝ := 4 * Real.pi * 11 - (Real.log phi + deltaKappa)
  45
  46end Curvature
  47
  48end Pipelines
  49end IndisputableMonolith